Estimation of amplitude and phase of a weak signal by using the property of sensitive dependence on initial conditions of a nonlinear oscillator

A new method is presented to determine the amplitude and phase of a weak signal by using a fundamental property of a nonlinear dynamical system, namely, the sensitive dependence on initial conditions (SDIC), given that some a priori knowledge about the signal order of magnitude is available. The corresponding bifurcation process for the Duffing oscillator is discussed in detail, and the Floquet exponents are employed to represent SDIC quantitatively. To show the efficiency of the present method, simulation results for the reconstruction are given and compared with those obtained by the maximum likelihood (ML) method. The robustness of the present method against variations of some experimental conditions is addressed.

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